The main objective of the present paper is to study the propagation of waves in the transversely isotropic medium in the context of thermoelasticity with GN theory of type-II and III. By imposing the boundary conditions on the components of displacement, stresses and temperature distribution, wave equation have been solved. Numerically simulated results have been plotted graphically with respect to frequency to evince the effect of anisotropy. Keywords: Thermoelasticity, transversely isotropic, reflection, plane wave AMS 2010 No.: 74JXX, 74F, 74B, 80A. 1. Introduction In last three decades, non-classical theories involving finite speed of heat transportation in elastic solids have been developed to remove the paradox obtained in classical theory. These generalized theories involve a hyperbolic-type heat transport equation, in contrast to the conventional coupled thermo-elasticity theory (1967), which involves a parabolic-type heat transport equation, and are supported by experiments exhibiting the actual occurrence of wavetype heat transport in solids, called second sound effect. The extended thermo-elasticity theory proposed by

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